A natural way to discover data properties is to study the underlying probability density function (pdf). Parametric and non-parametric models [1]} are viable solutions for density estimation problems that deal with low-dimensional data. The former are typically used when a prior knowledge on the data structure (e.g. distribution family) is available. The latter, instead, are more flexible since they do not require any specification of the distribution's parameters. Practically, the majority of methods from both classes fail in estimating high-dimensional densities. Hence, some recent works leveraged deep neural networks as density estimators [2]}, [3]}.
Although significant efforts have been made to scale neural network architectures in order to improve their modeling capabilities, most of tasks translate into conditional distribution estimations.
Instead, generative models attempt to learn the a-priori distribution to synthesize new data out of it. Deep generative models such as generative adversarial networks [4]}, variational autoencoders [5]} and diffusion models [6]}, tend to either implicitly estimate the underlying pdf or explicitly estimate a variational lower bound, providing the designer with no simple access to the investigated pdf.
